Math Solutions

(Solution Library) A certain system can experience three different types of defects. Let Ai, i = 1, 2, 3 denote the event that the system has a defect of type i.

Question: A certain system can experience three different types of defects. Let Ai, i = 1, 2, 3 denote the event that the system has a defect of type i. Suppose that

P(A 1 ) = 0.14, P(A 3 ) = 0.12, P(A 1 U A 3 ) = 0.2,

P(A 2 U A 3 ) = 0.18, P(A 2 \(\cap \) A 3 ) = 0.04, P(A 1 U A 2 U A 3 ) = 0.21.

  1. What is the probability that the system does not have a defect of type 1?
  2. What is the probability that the system has a type 1 defect but not a type 3 defect?
  3. What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect?
  4. What is the probability that the system has a type 2 defect?
  5. What is the probability that the system has at least one of these defects?
  6. What is the probability that the system has none of these defects?

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